Reactor assemblies and methods of performing reactions

ABSTRACT

Reactors are provided that can include a first set of fluid channels and a second set of fluid channels oriented in thermal contact with the first set of fluid channels where the channels of either one or both of the first of the set of fluid channels are non-linear. Reactor assemblies are also provided that can include a first set of fluid channels defining at least one non-linear channel having a positive function, and a second set of fluid channels defining at least another non-linear channel having a negative function in relation to the positive function of the one non-linear channel of the first set of fluid channels.

STATEMENT AS TO RIGHTS TO INVENTIONS MADE UNDER FEDERALLY-SPONSOREDRESEARCH AND DEVELOPMENT

This invention was made with Government support under ContractDE-AC05-76RL01830 awarded by the U.S. Department of Energy. TheGovernment has certain rights in the invention.

TECHNICAL FIELD

The present disclosure relates to reactor assemblies and methods forperforming reactions. Embodiments of the disclosure related toperforming endothermic reactions. Embodiments of the disclosure can alsoutilize solar energy or other heat sources to drive the endothermicreactions.

BACKGROUND

In the case of hydrogen production, current commercial technologiesinclude conventional steam methane reforming in systems that combust aportion of the product stream in order to drive the endothermicreaction, and water electrolysis where the energy for theelectrochemical reaction typically comes from the electrical grid. Solarthermochemical production of hydrogen from natural gas or other sourcesof methane can have the advantage of greater overall energy efficiencyand reduced carbon emissions compared to conventional steam-methanereforming and water electrolysis using grid electricity.

Reactor systems have been designed for steam reforming of methane andother hydrocarbons using concentrated solar power. Reactor assembliesand methods have been provided that include U.S. Pat. No. 9,950,305issued Apr. 24, 2018, entitled “Solar Thermochemical Processing Systemand Method”, and U.S. patent application Ser. No. 15/950,068 filed Apr.10, 2018, entitled “Solar Thermochemical Processing System and Method”,the entirety of each of which is incorporated by reference herein.

SUMMARY OF THE DISCLOSURE

Reactors are provided that can include a first set of fluid channels anda second set of fluid channels oriented in thermal contact with thefirst set of fluid channels. The channels of either one or both sets offluid channels can be non-linear.

Stacked reactor assemblies are also provided that can include first andsecond sets of fluid channels in a stacked configuration with the fluidchannels oriented in thermal contact with each other, and at least oneof the first set of fluid channels being in thermal contact with aplurality of other channels of the second set of fluid channels.

Reactor assemblies are also provided that can include a first set offluid channels defining at least one non-linear channel having a shapedefined by a positive mathematical function, and a second set of fluidchannels defining at least another non-linear channel having a shapedefined by a negative mathematical function in relation to the positivemathematical function of the one non-linear channel of the first set offluid channels.

Processes for distributing energy across a reactor are provided. Theprocesses can include transporting reactants via a first set of fluidchannels to a second set of fluid channels, and thermally engaging atleast one of the first set of fluid channels with at least two of thesecond set of fluid channels.

Embodiments of the present disclosure can utilize thermal energy tofacilitate or drive an endothermic reaction in at least one of the setsof fluid channels. In particular embodiments, heat for the channels canbe provided from a variety of sources, including electrical heating,exothermic chemical processes, and/or solar energy. Reactors and/ormethods can provide a high temperature endothermic reaction such asmethane steam reforming or reverse-water gas shift where the heat ofreaction is largely provided by solar energy. The reactors and/ormethods of the present disclosure have applications in syngasgeneration, which can be a precursor for the production of manychemicals, including hydrogen which can be useful in refineries, forfuel cells including fuel cell vehicles, and in other chemicalprocessing applications.

Reactor assemblies and/or methods of the present disclosure can have twosets of spiral shaped fluid channels that can be separated by a thinmember and arranged in opposite spiral directions to form a cross flowpattern, a counterflow pattern, or a counter-cross-flow pattern. Eachset can be an array of repeating non-linear units that define one ormultiple channels of spiral flow paths. The axes of symmetry of the twochannel groups can coincide at a hub. While the repeating units for eachfluid channel can be the same or different, according to exampleembodiments the repeat units can be different. The non-linear fluidchannels forming the repeat unit of the array can be derived from ageneral curve of a spiral nature, the curve being either planar or3-dimensional. While many types of spiral curves can be used,Archimedean and logarithmic spirals and their 3-dimensional derivativesare particularly relevant.

The integration of non-linear fluid channels and/or non-linearcounter-flow or non-linear counter-cross-flow channels can provide twobenefits which translate to performance and economic advantages. First,the combination can provide thermal spreading which, as described below,reduces the severity of hot spots and thermal stress, warms cold spots,and improves reactor lifetime. Second, the combination can allow for therecuperation of thermal energy (sensible heat) from the product streamto provide additional heat for the reaction. This may lower the amountof solar energy required for a given amount of reaction and thereforemakes the reactor system more efficient, more productive and lesscostly.

DRAWINGS

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawing(s) will be provided by the Office upon request and paymentof the necessary fee.

Embodiments of the disclosure are described below with reference to thefollowing accompanying drawings.

FIG. 1 is a cross sectional view of a reactor assembly according to anembodiment of the disclosure.

FIG. 2 is a view of a set of channels of a reactor assembly according toan embodiment of the disclosure.

FIG. 3 depicts two sets of reactor channels in a stacked configurationaccording to an embodiment of the disclosure.

FIG. 4 depicts two sets of reactor channels in a stacked configurationaccording to an embodiment of the disclosure.

FIGS. 5A-5D are portions of a configuration and an entire configurationof a reactor assembly according to an embodiment of the disclosure.

FIG. 6 is a view of a configuration and an entire reactor within theconfines of (r, θ) coordinates according to an embodiment of thedisclosure.

FIG. 7A is a depiction of a reactor shown with partial cut away portionsaccording to embodiment of the disclosure.

FIG. 7B is a depiction of a reactor shown with one fluid channel in afirst set of fluid channels in thermal contact with a plurality of fluidchannels in a second set of fluid channels.

FIG. 8 is a reaction schematic according to an embodiment of thedisclosure.

FIG. 9 is a depiction of thermal flux distribution data according to anembodiment of the disclosure.

FIGS. 10A-10C are depictions of thermal and stress distribution dataaccording to embodiments of the disclosure.

FIGS. 11A-11C are depictions of thermal and stress distribution dataaccording to an embodiment of the disclosure.

FIG. 12 is reaction data according to an embodiment of the disclosure.

FIG. 13 is reaction data according to an embodiment of the disclosure.

DESCRIPTION

This disclosure is submitted in furtherance of the constitutionalpurposes of the U.S. Patent Laws “to promote the progress of science anduseful arts” (Article 1, Section 8).

It has been recognized that for practical solar concentrators, there canbe hot spots at the reactor surface due to imperfections in the solarconcentrator optics. The hot spots, or local points of high solar flux,can limit the maximum total operating flux because of reactor metallurgylimits. Hot spots, or other thermal gradients, can also induce largethermal stresses in the reactor which can lead to reduced life time overthermal cycles due to low cycle fatigue. Thus, the differentialtemperatures associated with thermal gradients can lead to highoperating and/or capital costs and failures, causing reduced lifetimes,for the reactor system.

The present disclosure will be described with reference to FIGS. 1-13.Referring first to FIG. 1, a reactor 10 is shown in accordance with onecross section that includes a first set of fluid channels 12 in astacked configuration above a second set of fluid channels 14. Thesefluid channels can be in thermal contact with one another via member 16.In accordance with example implementations, one or both of the sets ofthese channels can include fluid channels that are non-linear. Inaccordance with other implementations, one of the channels of the firstset of fluid channels can be in thermal contact with a plurality ofother channels of the second set of fluid channels. As shown in FIG. 1,reactor 10 can include a flow of reactants to the first set of fluidchannels that traverse across a length of member 16 and then through afluid passageway to the second set of fluid channels 14, and then exitthe reactor after traversing member 16.

Referring next to FIG. 2, one example of non-linear channels 20 areshown. Non-linear channels 20 can emanate from hub 22 to rim 24 of areactor and non-linear channels 20 may have a dividing member 28therein. Non-linear channels 20 in combination with dividing member 28can form a pair of fluid passageways 30, for example. The channels canbe microchannels or mesochannels. A microchannel may be of any length inthe general direction of bulk flow and has one dimension, e.g., thewidth, that is typically in the direction of heat and/or mass transportand is greater than or equal to 1 micron and less than or equal to 1millimeter. A mesochannel may be of any length in the general directionof bulk flow and has one dimension, e.g., the width, that is typicallyin the direction of heat and/or mass transport and is greater than 1millimeter and less than or equal to 1 centimeter.

Referring next to FIG. 3, in accordance with one example embodiment ofthe disclosure, non-linear channels 20 of one set of fluid channels canbe associated with another set of linear fluid channels 26, and thesechannels may be stacked upon each other in accordance with exampleimplementations.

Referring next to FIG. 4, a pair of non-linear channels 20 and 40 areshown in accordance with one configuration, providing for fluidcommunication at 42 of fluid channels 20 and 40. As shown, both channels20 and 40 are non-linear. As shown in FIGS. 5A-5D, non-linear channels20 and 40 can be associated to form at least a portion of a reactorassembly 50 with these channels emanating from a hub 22 and extending toa rim 24 of assembly 50. Within each of these channels can be a dividingmember 58. Dividing member 58 can extend toward rim 24 to form a pair offluid conduits. In accordance with example implementations, there can bea plurality of non-linear channels 52 as well as a plurality ofnon-linear channels 54 that can form part of, or in the case of FIG. 5Dall of, reactor 50. In accordance with example implementations, this maybe considered a spiral channel design.

Referring next to FIG. 6, sets of non-linear channels are shownemanating from hub 22 to a rim 24 of a reactor. These channels are shownaligned along an example polar coordinate system 110 wherein the shapeof non-linear channels 60 can be considered to have a positivemathematical function about the coordinate system, while the shape ofnon-linear channels 80 can be considered to have a negative mathematicalfunction about the coordinate system.

The mathematical functions defining the channel shape and orientationcan be expressed by the general equation θ=ƒ(r) in reference to thepolar coordinate system 110 with coordinates (r, θ) in FIG. 6, where ƒis an arbitrary function that defines specific curvatures. For example,Archimedean spiral and similar curves are given by θ=((r−b)/a)^(c);logarithmic spiral curves are given by θ=(ln r−ln a)/b; linear lines aregiven by θ=d, where a, b, c, and d are parameters of arbitraryconstants. For the set of nonlinear channels 60 described by a positivefunction θ=ƒ(r) about the polar coordinate system 110, the correspondingset of channels 80 can be described by a related negative functiondefined by θ=−ƒ(r). More generally, one set of nonlinear channels can bedefined by a positive function θ=ƒ₁(r) and the other set of nonlinearchannels can be defined by a negative function θ=−ƒ₂(r), wheremathematical functions ƒ₁ and ƒ₂ may or may not be identical.Furthermore, the mathematical functions describing the shape ofnon-linear channels can be three-dimensional space curves in nature, inwhich case a general function θ=ƒ(r, z) in reference to a cylindricalcoordinate system (r, θ, z) can substitute θ=ƒ(r) in the proceedingdiscussion without loss of generality.

In accordance with example implementations, the non-linear mathematicalfunctions of the shape of fluid channels 60 and 80 when taken asabsolute values can be equal to one another, thereby having a mirrorimage of one another. In accordance with other implementations, thefluid channels may not be mirror images of each other but may still beconfigured as counter spirals. In accordance with exampleimplementations, reactors can include a plurality of non-linear fluidchannels having the same positive function as well as a plurality ofnon-linear channels having the same negative function. The reactor caninclude an entirety of one set of non-linear channels having a positivefunction and another set of non-linear channels having a negativefunction. In accordance with example implementations, and with referenceto FIG. 7A, reactor 200 is shown that includes an inlet 202 and anoutlet 204. Reactor 200 can include a first set of fluid channels 212 aswell as a second set of fluid channels 214 that are coupled at fluidpassageways 230, for example. With the exception of passageways 230,between sets of fluid channels 214 and 212, can be a member 216. Thiscan be a thermally conductive member that can also form the ceiling ofthe first set of fluid members 212 as well as the floor of the secondset of fluid channels 214. In accordance with example implementations,at least a portion of channels 212 may be provided with a catalyst, forexample, to facilitate reactions as desired. The catalyst can be packedinto either or both sets of channels in the form of foams, felts,lattices, or particles, for example. The catalyst can also be coated tochannel walls, which including part of member 216, which forms the floorof one set of channels and ceiling of the other set.

In accordance with example implementations, catalyst supported on foamcan be provided into one set of channels 212. In accordance with exampleimplementations, and with reference to individual fluid channels of oneset 212, an individual fluid channel of reactor 200 can be in thermalconnection with as many as two if not as many as 14 individual channelsof the other set 214, as shown as a plurality of contact at 206.

The process can provide transporting reactants via a first set of fluidchannels and extracting products from a second set of fluid channels andthermally engaging at least one of the first set of fluid channels withat least two of the second set of fluid channels as shown, for example,in FIG. 7A. In accordance with example implementations, an endothermicreaction can be provided in one of these sets of fluid channels, forexample, fluid channels 212 can have reactants provided thereto and bean endothermic reaction which can require facilitating the endothermicreaction with solar energy as shown in FIG. 8. In accordance withexample implementations, the reactor of FIG. 7A has a portion not shown(under portion or face) that can be exposed to solar energy to provideenergy to facilitate or drive this endothermic reaction. In accordancewith other implementations, as the reaction proceeds through thereactor, and heated products return via the set of fluid channels 214,the heat of these products is transmitted via member 216 to theendothermic reaction within channels 212.

While embodiments of the present disclosure can utilize most metals asthe material of construction, metals comprising Ni, Cu, stainless steelalloys, Ti, Ti alloys, super alloys such as Inconel, Hastelloy andHaynes alloys, and combinations thereof can be utilized. Ceramics mayalso be useful.

The dividing member 216 between the sets of channels can have a flat,concave, or convex contour. The dividing member can be any thicknessnecessary to support the channel structure and to provide a heatconduction path. In accordance with example implementations, thedividing member may have a thickness between 0.1 and 3.2 mm. Thedividing member can be an impermeable solid.

Heights of the individual channels within each set can be less than 100microns (0.1 millimeters) or greater than 1 centimeter. However, inembodiments where a solid catalyst is used, the channel heights arepreferably greater than 1 mm, and still more preferably greater than 5mm, in order to provide sufficient catalyst material to supportreactions.

Referring next to FIG. 8, a schematic is depicted for providingreactants and receiving products from reactors of the presentdisclosure. Accordingly, a process is provided for distributing energyacross a reactor such as the reactors herein.

In particular embodiments and with reference to FIG. 7A, a feed gasmixture of methane and steam enters reactor 200 at inlet 202 at the huband are distributed into a set of identical channels 212 with non-linearside walls. The channels traverse approximately one reactor radius andcan changes its direction by 90 or more degrees from start to finish. Ineach of the channels, a catalyst is present. This catalyst media maytake the form of a foam, conforming to the channel shape, but may alsoinclude a substrate maintained in the channel such as particles. Eachreaction channel can bifurcate at a short distance from the center sothat the catalyst media inserts are sufficiently broad near the hub.

Near the reactor rim where the channels end, slot shaped openingsconnect the channels to a second set of channels that curve in theopposite direction of that of the first set of channels. The second setof channels 214 may be referred to as heat recuperation channels whilethe first set of channels can be referred to as reaction channels. Thereaction channels and the heat recuperation channels are separated by asolid intermediate member 216 that allows heat transfer by conduction.The slot-shaped openings 230 penetrate the intermediate member to allowthe reaction product streams from the reaction channels to enter theheat recuperation channels. The product streams are returned to thecenter through the heat recuperation channels and flow out of thereactor through the annular space 204 between the inlet and the outletconnection tubes. Similar to the reaction channels, the heatrecuperation channels may also be bifurcated.

The spiral counter-cross flow pattern of this reactor is clearly shownin FIGS. 5D and 7A, where a 3-dimensional model of the reactor isrendered in wireframe style. The reactor structure can be describedalternatively by a sequence of repeating a single flow path in acircular pattern, as illustrated in FIGS. 4-5D in isometric views:

-   -   1. Start with one spiral heat recuperation channel, i.e. half of        a flow path.    -   2. Add one reaction channel of opposite spiral direction.    -   3. Connect the reaction channel and the heat recuperation        channel by a slot opening between them near the reactor        perimeter. The reaction channel is shown without catalyst and        with part of its top wall removed for clarity.    -   4. Repeat the heat recuperation channel in a circular pattern.    -   5. Repeat the reaction recuperation channel in a circulation        pattern.    -   6. Complete the patterns to a full circle, producing one group        of spiral reaction channels and one group of heat recuperation        channel in opposite spirals, arranged in counter flow.

Reactive flow under steam methane reforming conditions and non-uniformsolar flux distribution of embodiments of the present reactor assemblyand methods can be simulated to understand the effects of reactorgeometry and channel configuration on temperature and thermomechanicalstress distributions.

In one embodiment, the reactor provides thermal spreading over a largereactor area and multiple channels. The non-linear revolution can be onequarter or more of a full circle. In one embodiment incorporatingcounter-cross flow, the two sets of channels can cover a substantialarea of the reactor, thus using the fluid to provide substantial thermalspreading from hot zones to colder zones.

Each feed stream flowing in channels 212 is in thermal contact throughdividing member 216 with a plurality of product streams in the counterflow channels 214, the flow path of the latter group of streams coverapproximately one-fifth of the entire area between the two sets of flowchannels. Referring to FIG. 7B, the red area is occupied by feed streamin one channel. The yellow area is the portion of the flow paths of allproduct streams flowing cross the said feed stream. Thus the yellow arearepresents the extent of heat spreading afforded to each single channel.This area is 18% of the entire area between hub and rim.

The counter-cross flow arrangement of reaction channels and recuperativechannels can provide efficient thermal spreading of inhomogeneous solarirradiation to a substantially greater degree than could be provided bydirect thermal conduction through metal layers. The reduction of hotspots leads to lower operating and capital costs through improvements toreactor's operability under high flux conditions and longer reactor lifeby reducing thermal stress, respectively.

The solar flux distribution on the reactor surface can be estimated froma moon flux distribution obtained in previous experiments through amapping exercise where the parabolic dish was pointed at a full moon.The results are shown in FIG. 9 in W/m² where multiple hot spots areclearly present. This flux distribution was specified as a boundarycondition on the reactor front face for simulation models. Reactorshaving non-linear channels of the present disclosure and a previousdesign of radial counter flow linear channels with otherwise similarreactor and channel dimensions were simulated for comparison. The linearreactor and the non-linear reactor models are shown in FIGS. 10A-10C,and 11A-11C respectively.

The reactor surface temperature distributions under a set of typicalhigh solar flux conditions (9.6 kW total incident solar power, >80%methane conversion, 0.032 mol/s methane flow, steam to carbon ratio of3) are shown in FIGS. 10B and 11B, respectively, for the linear reactorand the non-linear reactors. The maximum surface temperature was foundto be 988° C. in the case of the non-linear, spiral counter-cross-flowreactor, over 100° C. reduction from the maximum surface temperature of1114° C. in the case of the linear reactor. Visually, the hot regions onthe surface of the non-linear reactor are spread out more evenly than onthe linear reactor. The superior thermal spreading by the non-linearreactor is attributed to the crossing of any reaction channels under ahot spot by multiple recuperation channels downstream of the hot spotwith the greater amount of received heat then being spread to otherchannels rather than back to the same channel. Conceptually, the thermalspreading in the linear reactor can be limited to the area of one wedgeshaped reaction channel, or about 5% of total surface area. The thermalspreading in the non-linear reactor is over at least an area enclosed bya reaction channel and its connected heat recuperation channel, or up toabout 18% of total surface area.

The von Mises stress in psi units is given in FIGS. 10C and 11C, for thelinear reactor and the non-linear reactor, respectively. The non-linearreactor has lower maximum stress than the linear reactor. The differencemay be attributed to thermal spreading and the resulting lowerthermomechanical stress.

One embodiment of the present disclosure was tested in a solarthermochemical reaction system that consisted of a solar concentrator ofthe parabolic dish type, an on-sun reactor unit located at the focalpoint of the dish, and the balance of plant located on the ground. Theconfiguration of the reaction system is given in FIG. 8. The on-sunreactor unit included a steam methane reforming reactor, recuperativeheat exchangers, water vaporizer, and onboard process controllers. Feedgas system, water pump, process analytical equipment, and tail gas flarewere on the ground. The feed gas was controlled using a mass flowcontroller. A methane stream was preheated by the network ofrecuperative heat exchangers using the product stream. Concentratedsolar energy was absorbed by the reforming reactor to convert methane tosyngas catalytically. The syngas product stream was cooled by the feedgas stream and additional air cooling. The compositions of the productgas were analyzed by a process gas chromatograph. The product stream wasvented through a flare after condensed water was separated.

A non-linear reactor, designated TRL 6, was manufactured according thedesign described in previous sections. In this particular embodiment ofthe disclosure, the reactor was fabricated by machining individualplates and diffusion bonding the stack of the plates. The reactor wastested under medium to high solar flux conditions with pairing to anInfinia PowerDish III parabolic dish concentrator with nominal mirrorarea of 14.85 m². A linear reactor of otherwise similar reactor andchannel dimensions, designated TRL 5, was also fabricated and testedon-sun with a dish concentrator of the same specifications.

With reference to FIGS. 12 and 13, the reactor performance was evaluatedby the energy conversion efficiency both at the reaction system level,i.e. the reactor and its heat exchanger network plus the dishconcentrator, and at the reactor component level, i.e. just the reactoritself. The system solar-to-chemical energy efficiency is defined as theratio of the higher heating value difference between the reactor productstream and the feed stream to the direct-normal solar energy incident(DNI) upon the dish concentrator reflector and therefore includeseffects due to mirror reflectivity, receiver intercept, heat lossesaround the reactor-receiver, and approach to equilibrium chemicalconversion in the reactor. The system solar-to-chemical energyefficiency data from the on-sun testing are given in FIG. 12.

System solar-to-chemical energy efficiency as high as upper 60% to 70%was achieved with the TRL 6 reactor system. This reactor system was ableto consistently achieve the high efficiency over medium to very highflux conditions. The excellent thermal spreading capacity of thenon-linear reactor design allowed the reaction channels to be at highertemperatures when the reactors were operated with the same surfacetemperature limit. The higher thermodynamic efficiency of theendothermic reaction at higher temperature is thought to be able to makeup any additional radiative heat lost, thus the overall highsolar-to-chemical conversion efficiency of TRL 6 reactor was able toextend to the high flux region.

As a comparison, due to the absence of enhanced thermal spreading, theTRL 5 reactor system was not operated at the same high solar flux as thenon-linear reactor system due to the surface temperature exceedingdesign points. In low to medium solar flux range, the non-linear reactorsystem also outperformed the linear reactor in terms ofsolar-to-chemical energy efficiency.

The performance advantage of the non-linear reactor is even more evidentwhen the energy efficiency of the reactor is examined. The reactorthermal-to-chemical efficiency is defined as the ratio of the higherheating value difference between the reactor product stream and the feedstream to the amount of concentrated solar thermal energy received bythe reactor and therefor includes effects due to heat losses around thereactor-receiver and the degree of chemical conversion in the reactor.The reactor thermal-to-chemical efficiency data from the on-sun testingare given in FIG. 13.

The TRL 5 reactor achieved 60%-70% thermal-to-chemical energy efficiencybut was limited to low to medium flux operation due to the hot spotissues and reactor material temperature limit. With the TRL 6 reactor,thermal-to-chemical energy conversion efficiency as high as 85% wasachieved in the high flux region. Some data points suggest even close to90% level performance may be possible. The non-linear reactor's superiorperformance in energy efficiency is attributed to its ability of greaterthermal spreading.

An exergy analysis was conducted based on TRL 6 reactor on-sunperformance data. The objective was to evaluate the reactor and the heatexchanger's second law efficiencies and to identify the sources andmagnitudes of exergy destruction. In the exergy analysis, the exergydestruction at the reactor front surface was estimated by approximatingthe surface temperature with an average value based on IR thermographymeasurements. The reference environment was chosen as 25° C. and 1 atmwith chemical compositions as proposed by Szargut et al. The TRL 6reactor's exergetic efficiency was determined to be greater than 90%.For example, when tested under conditions of 0.048 mol/s methane feedflow rate, steam to carbon ratio of 2.2, 10.88 kW concentrated solarpower input, and an average reactor surface temperature of 820° C., thereactor rate of exergy destruction was estimated to be 5.34 kW, giving areactor exergetic efficiency of 90.2%.

In compliance with the statute, embodiments of the invention have beendescribed in language more or less specific as to structural andmethodical features. It is to be understood, however, that the entireinvention is not limited to the specific features and/or embodimentsshown and/or described, since the disclosed embodiments comprise formsof putting the invention into effect. The invention is, therefore,claimed in any of its forms or modifications within the proper scope ofthe appended claims appropriately interpreted in accordance with thedoctrine of equivalents.

The invention claimed is:
 1. A reactor comprising: a first set of fluidchannels defining at least one non-linear channel having a shape definedby, with reference to a polar coordinate system, a positive mathematicalfunction; and a second set of fluid channels defining at least anothernon-linear channel having a shape defined by, with reference to thepolar coordinate system, a negative mathematical function in relation tothe positive mathematical function of the one non-linear channel of thefirst set of fluid channels.
 2. The reactor of claim 1 wherein the firstset of channels define microchannels.
 3. The reactor of claim 1 whereinthe first set of channels define mesochannels.
 4. The reactor of claim 1wherein the first and second set of channels define microchannels. 5.The reactor of claim 1 wherein the first and second set of channelsdefine mesochannels.
 6. The reactor of claim 1 wherein the absolutevalue of the mathematical function of the one channel is equivalent tothe absolute value of the mathematical function of the other channel. 7.The reactor of claim 1 wherein the first set of fluid channels defines aplurality of non-linear channels having the same positive mathematicalfunction; and the second set of fluid channels defines a plurality ofnonlinear channels having the same negative mathematical function inrelation to the positive mathematical function of the plurality ofnon-linear channels of the first set of fluid channels.
 8. The reactorof claim 7 wherein the absolute value of the mathematical function ofthe plurality of non-linear channels of the first set of fluid channelsis equivalent to the absolute value of the mathematical function of theplurality of non-linear channels of the second set of fluid channels. 9.The reactor of claim 1 wherein each of individual ones of the first setof fluid channels defines a non-linear channel having the positivemathematical function; and each of individual ones of the second set offluid channels defines a non-linear channel having the negativemathematical function in relation to the positive mathematical functionof the individual non-linear channels of the first set of fluidchannels.
 10. The reactor of claim 9 wherein the absolute value of themathematical function of the individual non-linear channels of the firstset of fluid channels is equivalent to the absolute value of themathematical function of the individual non-linear channels of thesecond set of fluid channels.
 11. The reactor of claim 1 wherein thefirst set of fluid channels are curves given by the formulaθ=((r−b)/a)^(c).
 12. The reactor of claim 11 wherein the second set offluid channels are curves given by the formula θ=−((r−b)/a)^(c).
 13. Thereactor of claim 1 wherein the first set of fluid channels defining atleast one non-linear channel comprise a three dimensional curve.
 14. Thereactor of claim 1 wherein the first set of fluid channels and thesecond set of fluid channels are configured as counter spirals.
 15. Thereactor of claim 1 wherein either or both sets of channels comprise acatalyst.
 16. The reactor of claim 15 wherein the catalyst is in theform of foams, felts, lattices, or particles.